Answer:
(-1,-1)
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Answer:
x= -1 and y= -1
Step-by-step explanation:
Power through with me as I explain this, its a bit long of an explanation.
To solve the following system of equations, we need to write 5x-4y=-1 in slope-intercept form.
[tex]5x -4y= -1[/tex]
Subtract 5x from both sides.
[tex]5x-5x -4y= -1 -5x[/tex]
[tex]-4y= -1-5x[/tex]
Divide each term by -4.
[tex]\frac{-4y}{-4} = \frac{-1}{-4} + \frac{-5x}{-4}[/tex]
Remember that dividing two negative values results in a positive value.
[tex]y= \frac{1}{4} + \frac{5x}{4}[/tex]
Reorder the terms. (Reordering terms makes the work tidier, it does not change the result)
[tex]y= \frac{5}{4} x+ \frac{1}{4}[/tex]
Now that we have the slope-intercept form, we can solve by subsitution with the two equations to find the solution.
Substitute [tex]\frac{5}{4} x + \frac{1}{4}[/tex] for y in [tex]y= 6x+5[/tex].
[tex]\frac{5}{4} x+\frac{1}{4} = 6x + 5[/tex]
Subtract 1/4 from each side.
[tex]\frac{5}{4}x+\frac{1}{4}-\frac{1}{4}=6x+5-\frac{1}{4}[/tex]
Simplify the left side.
[tex]\frac{5}{4}x=6x+5 -\frac{1}{4}[/tex]
Simplify the right side.
[tex]\frac{5}{4}x=6x+\frac{19}{4}[/tex]
Subtract 6x from both sides.
[tex]\frac{5}{4}x-6x=6x+\frac{19}{4}-6x[/tex]
Simplify.
[tex]\frac{5}{4}x-6x=\frac{19}{4}[/tex]
Simplify the left side of the equation by factoring out x.
[tex]x(\frac{5}{4} -6)= \frac{19}{4}[/tex]
[tex]x(-\frac{19}{4} )=\frac{19}{4}[/tex]
[tex]-\frac{19}{4} x=\frac{19}{4}[/tex]
Multiply each side by 4.
[tex]4\left(-\frac{19}{4}x\right)=\frac{19*4}{4}[/tex]
[tex]-19x=19[/tex]
Divide both side by 19.
[tex]\frac{-19x}{-19}=\frac{19}{-19}[/tex]
[tex]x= -1[/tex]
Now that we know the value of x, we need to find y.
Insert the value of x in the equation y= 6x+5
[tex]y= 6(-1) +5[/tex]
[tex]y=-6+5[/tex]
[tex]y=-1[/tex]
Thus, x= -1 and y= -1 OR (-1,-1)
